Benedict Cumberbatch and Jonny Lee Miller were the last to do it when they alternated as Frankenstein and the monster at the National. Now Kristin Scott Thomas and Lia Williams continue the long and honourable theatrical tradition of swapping roles in Ian Rickson's highly compelling revival of Harold Pinter's 1971 play 'Old Times'.

Depending on which performance you see, each actress will portray either Kate, the wife of a film director (played by Rufus Sewell) or Anna, an old flatmate of Kate's from her London days, who visits the couple after a 20 year gap at their seaside home.

The switching is not designed to force a particular reading on the play or to endorse the view (wrong-headed in my opinion) that Kate and Anna are dual aspects of the one woman.

But it does illustrate how the shift in casting-chemistry can put a different complexion on what is broadly the same interpretation of the piece and intriguingly alter the dynamic of Pinter's play – a three-hander in which the husband, threatened by his feeling of exclusion from Anna's accounts of a togetherness that pre-dates him, fights with her for possession of the mysteriously withdrawn and incurious Kate.

The weapons the pair use are rival memories (with which of them did Kate see the aptly named movie 'Odd Man Out'?) that are always subject to revision or blatant invention according to the strategic needs of the moment in the struggle to assert a superior intimacy.

When Williams's Anna lays claim to the 'Odd Man Out' experience at the end of a gushing speech about the girls' arty exploits in London, she emphasises the point by emitting a triumphant puff of smoke that's like a declaration of war. Scott Thomas's Anna is slyly amused, at that point, and helps herself to another brandy.

To see both alternatives is to appreciate the impact that small changes of detail and emphasis such as that can have. They accumulate so that larger ones also make sense. When Kate eventually turns on her friend and goes for the jugular ('I remember you dead'), Williams's Anna tumbles off the divan and has to stare up at her aggressor from an ignominiously discarded position on the floor. Scott Thomas takes her punishment standing up.

I'm afraid I cannot avoid being invidious when I say that, for me, both of Scott Thomas's performances are wonderfully free from the mannered portentousness than can afflict productions of Pinter's plays in general and of this one in particular. As Kate, she exudes remote beauty and Sphinx-like inscrutability but subtly lets you see the tremors of irritation and restiveness under the languor, especially when the other two talk about her as if she were dead.

As Anna, with her rather iffy secretary-made-good accent and her satiric send-up of arousing Deeley during the kinky talk about Kate's bath-time habits, she brings a wonderful almost vulgar comic verve to a character often played as too coolly contained.

Both of the actresses emphasise the risky improvisatory nature of Anna's nature rather than its calculation (more studiedly in Williams's case) and Rufus Sewell in each of these versions, brilliantly shows you a man who masks his insecurity behind a goading, flirtatiously joky knowingness.

'Old Times' is a play about which I have always had mixed feelings, but Rickson's haunting yet robust production with its fascinating casting ploy offers more positive reasons for being in two minds about it.